Nuprl Lemma : sum_of_torder_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. (sum_of_torder(T;R) ∈ ℙ)
Proof
Definitions occuring in Statement :
sum_of_torder: sum_of_torder(T;R),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
sum_of_torder: sum_of_torder(T;R),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
or: P ∨ Q,
so_apply: x[s]
Lemmas referenced :
all_wf,
or_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
because_Cache,
functionEquality,
productEquality,
applyEquality,
hypothesis,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (sum\_of\_torder(T;R) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-04_55_04
Last ObjectModification:
2015_12_27-PM-02_31_29
Theory : general
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